ical integrationsn± 1，2，3， where δe and δa are the absolute change of the total energy and total angular momentum， respectively， ande0anda0are their initial values. the horizontal unit is gyr.
note that different operating systems， different mathematical libraries， and different hardware architectures result in different numerical errors， through the variations in round-off error handling and numerical algorithms. in the upper panel of fig. 1， we can recognize this situation in the secula